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On The Consistency Of Some Crisp Choice Functions Based On A Strongly Complete Fuzzy Pre-Order

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    (Département de Mathématiques, Ecole Normale Supérieure de Yaoundé, Université de Yaoundé I, B.P. 47 Yaoundé, Cameroun)



    (Département de Mathématiques et Informatique, Faculté des Sciences, Université de Douala, B.P. 24157 Douala, Cameroun)

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    This paper presents the first part of a general study of the structure of nine preference-based choice functions introduced by Barrett et al.2 More precisely, we show that, as for crisp total pre-orders, first and last alternatives exist in a finite set of alternatives equipped with a strongly complete fuzzy pre-order. We use that result to characterize each of those crisp choice functions for crisp total pre-orders and strongly complete fuzzy pre-orders. We study, by means of those characterizations, the consistency of those preference-based choice functions when preferences are strongly complete fuzzy pre-orders (thereby crisp total pre-orders), that is, we check if each choice function satisfies or violates each of six consistency conditions introduced by Sen.11

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    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal New Mathematics and Natural Computation.

    Volume (Year): 08 (2012)
    Issue (Month): 02 ()
    Pages: 257-272

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    Handle: RePEc:wsi:nmncxx:v:08:y:2012:i:02:p:257-272
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